Electron microscope and method for controlling focus position thereof

ABSTRACT

There are provided an electron microscope capable of carrying out focusing and astigmatism correction without depending on characteristics of a sample, and a method for controlling its focus position.  
     The electron microscope according to the present invention comprises: an electron optical system ( 2 ); a focus control part ( 3 ); an image detecting part ( 4 ); a first operating part ( 11 ) for mutually dividing first and second transformed images ( 9 ) and ( 10 ), which are obtained by carrying out the fast Fourier transform of first and second images ( 7 ) and ( 8 ) detected at two focus positions of a first focus position (f1) and a second focus position (f2) shifted from the first focus position by a known focus shifted quantity Δf, to obtain a measured divided quantity Rexp; divided quantity data ( 12 ) previously prepared and stored as a function of focus positions and spatial frequencies as a set of theoretical divided quantities, the theoretical divided quantities being obtained by substituting the two focus positions shifted by the focus shifted quantity Δf for an image transfer function (r,f) to obtain first and second transfer function values K(r;f) and (r;f+Δf) to mutually divide the first and second transfer function values K(r;f1) and (r;f+Δf) on a spatial frequency plane; and a second operating part ( 13 ) for making a reference to the divided quantity data ( 12 ) to derive a theoretical divided quantity K(r;f0) correlating to the measured divided quantity Rexp, and for deriving a focus position f0 corresponding to the derived theoretical divided quantity K(r;f0)/K(r;f0+Δf) as a first focus position f1.

TECHNICAL FIELD

[0001] The present invention relates generally to an electron microscopeand a method for controlling the focus position thereof. Morespecifically, the invention relates to an electron microscope capable ofautomatically correcting its focus position and astigmatism, and amethod for controlling the focus position.

BACKGROUND ART

[0002] In a case where the electron optical system of an electronmicroscope is intended to be automatically adjusted, it is not easy tocarry out automation similar to the automatic focusing function ofgeneral purpose optical cameras, video cameras or the like. The mainreasons for this include (1) problems on S/N ratio and (2) aberrationcharacteristics.

[0003] The S/N ratio of electron microscope images is low unlike generalimages, so that the processing of the differential system of picturesignals does not function. If an image having a high S/N ratio isintended to be obtained, the dose of electron beams must be increased.However, the irradiation damage of a sample causes a problem, so thatthe adjusting method for acquiring many images further increases thisproblem. In addition, a high resolution must be achieved. Finally, evenif the S/N ratio is low, the processing of the differential system ofpicture signals must function. This makes the automatic adjusting methoddifficult.

[0004] The specific aberration characteristics of electron microscopesalso make the adjusting method difficult. In general purpose opticalcameras, only the focus may be adjusted. However, in the optical systemsof electron microscopes, astigmatism correction must be also adjusted inaddition thereto. Since there are two adjusting quantities (with respectto x and y directions) in the adjustment of astigmatism correction, theadjusting method is further complicated, so that it is difficult tocarry out the adjusting method. In addition, unlike optical lenssystems, spherical aberration can not be corrected except for veryspecial cases. Particularly in high resolution electron microscopes,optimum conditions can not be obtained on a so-called Gaussian plane.This also makes the adjusting method difficult.

[0005] Thus, the electron optical system can not easily adjusted, sothat it is desired to automate the adjustment of the electron opticalsystem.

[0006] In conventional three-dimensional electron microscopes, it isrequired to acquire many images in order to automatically adjust theelectron optical system. Naturally, it is required to obtain preciseseries images under the same optimum optical conditions, so that thereis a problem in that this is complicated and is not easily achieved.

[0007] Moreover, when obtained electron microscope images are utilizedfor carrying out focusing in conventional electron microscopes, electronmicroscope images are naturally reflected in characteristics of samples,such as compositions and shapes, so that it is not possible to recognizeelectron optical states from which characteristics of the samples areabstracted. For that reason, there is a problem in that it is notpossible to precisely carry out focusing since the degree of focusingdepends on characteristics themselves of the samples.

[0008] In addition, if astigmatism exists, it is required to correctastigmatism by a so-called stigmater while it is not possible toprecisely carry out focusing.

DISCLOSURE OF THE INVENTION

[0009] It is therefore an object of the present invention to eliminatethe above described problems in the prior art and to provide an electronmicroscope capable of simply, surely and automatically adjustingelectron optical parameters, such as precise focusing and astigmatismcorrection, and a method for controlling its focus position.

[0010] In order to accomplish the above described object, according toone aspect of the present invention, an electron microscope comprises:an electron optical system for conducting an electron beam to a sample;a focus control part for controlling a focus position of the electronoptical system with respect to the sample; an image detecting part fordetecting an image caused by the electron beam aimed at the sample;first operating means for spatial frequency changing each of first andsecond images, which are detected by the image detecting part at twofocus positions of a first focus position and a second focus positionwhich is a focus shifted from the first focus position and which isrealized by changing a predetermined physical quantity by a knownquantity, to obtain first and second transformed images to mutuallydivide the first and second transformed images on a spatial frequencyplane to derive a measured divided quantity indicative of dividedresults as a function of a spatial frequency; divided quantity datapreviously prepared as a function of focus positions and spatialfrequencies as a set of theoretical divided quantities, the theoreticaldivided quantities being obtained by deriving an image transfer functionwith respect to the electron optical system as a function of focuspositions and spatial frequencies, substituting the two physicalquantities, which are shifted from each other by the known quantity, forthe image transfer function to obtain first and second transfer functionvalues to mutually divide the first and second transfer function valueson a spatial frequency plane; and second operating means for making areference to the divided quantity data to derive the theoretical dividedquantities, wherein functional characteristics with respect to a spatialfrequency correlate to the measured divided quantity, and for deriving afocus position corresponding to the derived theoretical divided quantityas the first focus position, wherein the focus position of the electronoptical system is controlled by the focus control part on the basis ofthe operated results of the second operating means.

[0011] The predetermined physical quantity may be a focus position, andthe known quantity may be a focus shifted quantity between the first andsecond focus positions.

[0012] The first operating means may average the divided results toderive the measured divided quantity as a function of a one-dimensionalspatial frequency.

[0013] The first operating means may divide the divided results intosections of a range of values of spatial frequencies to average themevery one of the sections to derive the measured divided value as aone-dimensional spatial frequency every one of the sections, and thesecond operating means may make a reference to the divided quantity datato derive the theoretical divided quantity, in which functionalcharacteristics with respect to a spatial frequency correlate to themeasured divided quantity, every one of the sections to derive anaverage theoretical divided quantity of maximum and minimum theoreticaldivided quantities of the theoretical divided quantities derived everyone of the sections, to derive a focus position corresponding to theaverage theoretical divided quantity as the first focus position. Theelectron microscope may further comprise a stigmater for correctingastigmatism, and astigmatism may be corrected by the stigmater.

[0014] According to another aspect of the present invention, an electronmicroscope comprises: an electron optical system for conducting anelectron beam to a sample; an astigmatism control part for controllingastigmatism of the electron optical system with respect to the sample;an image detecting part for detecting an image caused by the electronbeam aimed at the sample; first operating means for spatial frequencychanging each of first and second images, which are detected by theimage detecting part at two astigmatism quantity of a first astigmatismquantity and a second astigmatism quantity which is an astigmatismquantity shifted from the first astigmatism quantity and which isrealized by changing a predetermined physical quantity by a knownquantity, to obtain first and second transformed images to mutuallydivide the first and second transformed images on a spatial frequencyplane to derive a measured divided quantity indicative of dividedresults as a function of a spatial frequency; divided quantity datapreviously prepared as a function of astigmatism quantities and spatialfrequencies as a set of theoretical divided quantities, the theoreticaldivided quantities being obtained by deriving an image transfer functionwith respect to the electron optical system as a function of astigmatismquantities and spatial frequencies, substituting the two physicalquantities, which are shifted from each other by the known quantity, forthe image transfer function to obtain first and second transfer functionvalues to mutually divide the first and second transfer function valueson a spatial frequency plane; and second operating means for making areference to the divided quantity data to derive the theoretical dividedquantities, wherein functional characteristics with respect to a spatialfrequency correlate to the measured divided quantity, and for derivingan astigmatism quantity corresponding to the derived theoretical dividedquantity as the first astigmatism quantity, wherein the astigmatismquantity of the electron optical system is controlled by the astigmatismcontrol part on the basis of the operated results of the secondoperating means.

[0015] According to a further aspect of the present invention, there isprovided a method for controlling a focus position of an electronmicroscope, the method comprising: a step of conducting an electron beamto a sample; a first operating step of spatial frequency changing eachof first and second images, which are detected by an image detectingpart at two focus positions of a first focus position and a second focusposition, which is a focus shifted from the first focus position andwhich is realized by changing a predetermined physical quantity by aknown quantity, to obtain first and second transformed images tomutually divide the first and second transformed images on a spatialfrequency plane to derive a measured divided quantity indicative ofdivided results as a function of a spatial frequency, when an imagecaused by the electron beam aimed at the sample is detected by the imagedetecting part; a second operating step of deriving an image transferfunction with respect to the electron optical system as a function of afocus position and a spatial frequency, to substitute the two physicalquantities, which are shifted from each other by the known quantity, forthe image transfer function to obtain first and second transfer functionvalues to mutually divide the first and second transfer function valueson a spatial frequency plane, to obtain theoretical divided quantitiesto make a reference to divided quantity data, which are previouslyprepared as a function of a focus position and a spatial frequency as aset of the theoretical divided quantities, to derive a focus positioncorresponding to the derived theoretical divided quantities as the firstfocus position; and a step of controlling the focus position of theelectron optical system by a focus control part, which is provided forcontrolling the focus position of the electron optical system withrespect to the sample, on the basis of the results of operation at thesecond operating step.

[0016] In the method for controlling a focus position of an electronmicroscope, the predetermined physical quantity may be a focus position,and the known quantity may be a focus shifted quantity between the firstand second focus positions.

[0017] The first operating means may average the divided results toderive the measured divided quantity as a function of a one-dimensionalspatial frequency.

[0018] The first operating means may divide the divided results intosections of a range of values of spatial frequencies to average themevery one of the sections to derive the measured divided value as aone-dimensional spatial frequency every one of the sections, and thesecond operating means may make a reference to the divided quantity datato derive the theoretical divided quantity, in which functionalcharacteristics with respect to a spatial frequency correlate to themeasured divided quantity, every one of the sections to derive anaverage theoretical divided quantity of maximum and minimum theoreticaldivided quantities of the theoretical divided quantities derived everyone of the sections, to derive a focus position corresponding to theaverage theoretical divided quantity as the first focus position. Theastigmatism may be corrected by a stigmater.

[0019] According to a still further aspect of the present invention,there is provided a method for controlling an astigmatism quantity of anelectron microscope, the method comprising: a step of conducting anelectron beam to a sample; a first operating step ofspatial-frequency-changing each of first and second images, which aredetected by an image detecting part at two astigmatism quantities of afirst astigmatism quantity and a second astigmatism quantity, which isan astigmatism quantity shifted from the first astigmatism quantity andwhich is realized by changing a predetermined physical quantity by aknown quantity, to obtain first and second transformed images tomutually divide the first and second transformed images on a spatialfrequency plane to derive a measured divided quantity indicative ofdivided results as a function of a spatial frequency, when an imagecaused by the electron beam aimed at the sample is detected by the imagedetecting part; a second operating step of deriving an image transferfunction with respect to the electron optical system as a function of anastigmatism quantity and a spatial frequency, to substitute the twophysical quantities, which are shifted from each other by the knownquantity, for the image transfer function to obtain first and secondtransfer function values to mutually divide the first and secondtransfer function values on a spatial frequency plane, to obtaintheoretical divided quantities to make a reference to divided quantitydata, which are previously prepared as a function of an astigmatismquantity and a spatial frequency as a set of the theoretical dividedquantities, to derive an astigmatism quantity corresponding to thederived theoretical divided quantities as the first astigmatismquantity; and a step of controlling the astigmatism quantity of theelectron optical system by a focus control part, which is provided forcontrolling the astigmatism quantity of the electron optical system withrespect to the sample, on the basis of the results of operation at thesecond operating step.

[0020] In the above described invention, the first and second two imagesare detected at two focus positions, which are realized by changing thephysical quantity, such as a focus position, to compare the detectedresults with theoretical data to recognize the electron optical state ofthe electron microscope to automatically adjust the focus positionand/or focusing in the presence of astigmatism. Each of the first andsecond images obtained at the first and second two focus positions isspatial frequency changed to obtain first transformed images to mutuallydivide the first and second transformed images on the spatial frequencyplane, so that it is possible to eliminate the sample function O(x,y)depending the kind of the sample. The measured divided quantity isexpressed by information on only the electron optical state of theelectron optical system without depending on characteristics of variousspatial frequencies of the samples themselves, which are capable ofbeing possessed by various samples. As a result, it is possible toprecisely carry out focusing and astigmatism correction withoutdepending on characteristics of samples.

[0021] The same technique as that for detecting the first and second twoimages at two focus positions, which are realized by changing thepredetermined physical quantity by the known quantity, to compare thedetected results with theoretical data to recognize the electron opticalstate of the electron microscope to automatically adjust the focusposition can be applied for detecting first and second two images at twoastigmatism quantities, which are realized by changing a predeterminedphysical quantity by a known quantity, to compare the detected resultswith theoretical data to recognize the electron optical state of theelectron microscope to automatically astigmatism quantity.

BRIEF DESCRIPTION OF THE DRAWINGS

[0022]FIG. 1 is a block diagram showing a preferred embodiment of anelectron microscope, and a method for controlling its focus positionaccording to the present invention, wherein {circle over (1)}-{circleover (7)} show an operating procedure when focusing is carried out;

[0023]FIG. 2 is an illustration for explaining divided quantity data,wherein (a), (b), . . . , (h) denote K(r;f) at various focus positionsf, the divided quantity data being obtained as a set of theoreticaldivided quantities K(r;f)/K(r;f+Δf);

[0024]FIG. 3 is a diagram showing an operating procedure when focusingis carried out;

[0025] FIGS. 4(a-1) and 4(b-1) are diagrams showing a measured dividedquantity Rexp (a) in the absence of astigmatism and (b) in the presenceof astigmatism, respectively, and FIGS. 4(a-2) and 4(b-2) are diagramsshowing a one-dimensional radius vector counting histogram P(rj)obtained from a binary image B(rj, θi) (a) in the absence of astigmatismand (b) in the presence of astigmatism, respectively, wherein athreshold level suitably set on the one-dimensional radius vectorcounting histogram P(rj) is applied for obtaining the upper limit ofspatial frequency required when the fitting of Rave(r) to the dividedquantity data is carried out by the cross-correlation method;

[0026]FIG. 5(a) is a graph showing divided quantity data expressed byfocus positions f on the axis of abscissas and spatial frequencies onthe axis of ordinates, and FIG. 5(b) is a graph showing focus positionsf on the axis of abscissas and cross-correlation counts (XCC) on theaxis of ordinates when the fitting of Rave(r) to the divided quantitydata is carried out by the cross-correlation method, wherein the focusposition corresponding to the maximum cross-correlation coefficient(XCCmax) is obtained as a value of a focus position f1 which is bestcoincident;

[0027]FIG. 6 is a diagram showing an operating procedure when focusingis carried out in the presence of astigmatism;

[0028] FIGS. 7(a) and 7(d) are two HAADF-STEM images acquired atdifferent focus positions with respect to a thin-film sample of a DRAMbeing a semiconductor device, and FIGS. 7(b) and 7(e) are diagramsshowing power spectra obtained by carrying out the Fourier transform ofthe images of FIGS. 7(a) and 7(d), and FIG. 7(c) is a diagram showingmeasured divided quantities Rexp(u,v) obtained by division;

[0029]FIG. 8(a) is an HAADF-STEM image after automatic focusing, andFIG. 8(b) is a diagram showing power spectra obtained by carrying outthe Fourier transform of the image of FIG. 8(a);

[0030] FIGS. 9(a) through 9(e) shows diagrams in experiments onautomation of astigmatism correction, wherein FIGS. 9(a) and 9(d) aretwo HAADF-STEM images acquired at different focus positions with respectto an Au particle deposited sample on a carbon thin film, and FIGS. 9(b)and 9(e) are diagrams showing power spectra obtained by carrying out theFourier transform of the images of FIGS. 9(a) and 9(d), and FIG. 9(c) isa diagram showing measured divided quantities Rexp(u,v) obtained bydivision; and

[0031]FIG. 10(a) is an HAADF-STEM image after automatic astigmatismcorrection, and FIG. 10(b) is a diagram showing power spectra obtainedby carrying out the Fourier transform of the image of FIG. 10(a).

BEST MODE FOR CARRYING OUT THE INVENTION

[0032] Referring to the accompanying drawings, the preferred embodimentof an electron microscope and a method for controlling its focusposition according to the present invention will be described below.

[0033] The present invention is intended to detect first and second twoimages at two focus positions, which are realized by changing apredetermined physical quantity only by a known quantity, to compare thedetected results with theoretical data to recognize the electron opticalstate of an electron microscope to automatically adjust its focusposition and/or astigmatism. The predetermined physical quantity may beany physical quantity univocally influencing the focus position of theelectron microscope. The predetermined physical quantity should not belimited to the focus position, but it may be another physical quantity,e.g., an accelerating voltage of electron beams. In the followingdescriptions, the focus position itself will be used as an example of apredetermined physical quantity capable of being easily handled, and afocus shifted quantity between two focus positions is used as the knownquantity.

[0034] First, referring to FIG. 1, an electron microscope and a methodfor controlling its focus position according to the present inventionwill be schematically described.

[0035] As shown in FIG. 1, the electron microscope according to thepresent invention comprises: an electron optical system 2 for conductingelectron beams to a sample 1; a focus control part 3 for controlling afocus position f of the electron optical system 2 with respect to thesample 1; an image detecting part 4 for detecting an image caused byelectron beams aimed at the sample 1; a computer 5 for carrying outvarious operations and controls, and a stigmater 14 for correctingastigmatism.

[0036] The computer 5 comprises a first operating means 11 for carryingout the Fourier transform (FFT) (spatial frequency transformation) ofeach of first and second images 7 and 8 detected by the image detectingpart 4 at two focus positions, one of which is a suitably set firstfocus position f1 and the other of which is a second focus position f2shifted from the first focus position f1 by a known focus shiftedquantity Δf, to obtain first and second transformed images 9 and 10 tomutually divide the first and second transformed images 9 and 10 on aspatial frequency plane (u,v) to derive a measured divided quantity Rexpindicative of the divided results as a function of a spatial frequency.Herein, u and v denote spatial frequency variables of a rectangularcoordinate system.

[0037] The computer 5 has divided quantity data 12 which are previouslyprepared and stored as a function of a focus position and a spatialfrequency as a set of theoretical divided quantities K(r;f)/K(r;f+Δf).The theoretical divided quantities K(r;f)/K(r;f+Δf) are obtained byderiving an image transfer function K(r,f) with respect to the electronoptical system 2 as a function of a focus position and a spatialfrequency, substituting the above described two focus positions, whichare shifted by the focus shifted quantity Δf, for the image transferfunction K(r,f), obtaining a first transfer function value K(r;f) and asecond transfer function value K(r;f+Δf), and mutually dividing thefirst transfer function value K(r;f1) and the second transfer functionvalue K(r;f+Δf) on the spatial frequency plane (u,v). Herein, r denotesa spatial frequency variable of a polar coordinate system, and r²=u²+v².

[0038] The computer 5 further comprises a second operating means 13 formaking a reference to the divided quantity data 12 to derive atheoretical divided quantity K(r;f0)/K(r;f0+Δf) wherein functionalcharacteristics with respect to the spatial frequency correlate to themeasured divided quantity Rexp, and for deriving a focus position f0corresponding to the derived theoretical divided quantity(r;f0)/K(r;f0+Δf) as a first focus position f1.

[0039] Since the focus control part 3 is capable of deriving the firstfocus position f1 as an absolute position by the results of operationscarried out by the second operating means 13, the focus control part 13is designed to control an electron lens 15 and so forth of the electronoptical system 2 to focus the electron optical system 2 to obtain aclear formed image having an automatically adjusted focus.

[0040] The details of the above described contents will be describedbelow.

[0041] The present invention is intended to actually detect an electronoptical state to use the detected results to automatically adjust thefocus position and/or astigmatism, and is capable of automaticallyadjusting focusing regardless of the presence of astigmatism. Thefocusing in the absence of astigmatism, and the focusing in the presenceof astigmatism (focusing with correction of astigmatism) will bedescribed below.

[0042] First, referring to FIG. 2, the divided quantity data 12 will bedescribed below.

[0043] The transfer function K(u,v) with respect to the electron opticalsystem 2 can be theoretically obtained from the geometry of the electronoptical system 2. If the electron optical system 2 has a rotationsymmetry, K(u,v;f) can be indicated as K(r;f). In FIG. 2, (a), (b), . .. , (h) denote K(r;f) at various focus positions f. Since the electronoptical system 2 is axis-symmetric, K(r;f) is indicated as a ring-shapedpattern. Herein, r²=u²+v².

[0044] If Δf has been determined, K(r;f+Δf) data are derived from K(r;f)data, so that the theoretical divided quantities K(r;f)/K(r;f+Δf) withrespect to the focus position f can be theoretically easily calculated.The divided quantity data 12 is obtained as a set of theoretical dividedquantities K(r;f)/K(r;f+Δf) with respect to various focus positions f.In FIG. 2, each of reference numbers 12 a and 12 b denotes a part of thedivided quantity data 12. The axis of abscissas denotes focus positions(focus shifted quantities) f, and the axis of ordinates denotes spatialfrequencies r. The divided quantity data 12 has been previously derivedas a set of theoretical divided quantities K(r;f)/K(r;f+Δf) with respectto various focus positions f, and has been stored in a memory of thecomputer 5. Herein, Δf is the same quantity as the focus shiftedquantity Δf which is used when a measured divided quantity Rexp isobtained. Since an effective spectral region increases if Δf is not toowide and suitably set, Δf may be set to be about 1 to 2 [Sch].

[0045] The measured divided quantity Rexp will be described below.

[0046] It is assumed that the first and second images 7 and 8 detectedunder different electron optical conditions (different focus shiftedquantities) are I₁(x,y) 7 and I₂(x,y) 8, respectively. Between thetransfer function K(u,v) with respect to the electron optical system 2,and the Fourier transforms F[I₁(x,y)] 9 and F[I₂(x,y)] 10 of the twoimages I₁(x,y) and I₂(x,y), and the Fourier transform F[O(x,y)] withrespect to the sample function O(x,y) of the sample 1, the followingexpression is established.

F[I _(1.2)(x,y)]=F[O(x,y)]·K _(1.2)(u,v)  (1)

[0047] It should be noted that the measured divided quantity Rexpobtained by carrying out division between the F[I₁(x,y)] and F[I₂(x,y)]does not include the sample function O(x,y) and is expressed by a ratioof the values of the transfer functions K(u,v) at the respective focuspositions f1 and f2, as expressed by the following expression.$\begin{matrix}{{R\quad \exp} = {{{F\left\lbrack {I_{1}\left( {x,y} \right)} \right\rbrack}/{F\left\lbrack {I_{2}\left( {x,y} \right)} \right\rbrack}}\quad = {{K_{1}\left( {u,v,f_{1}} \right)}/{K_{2}\left( {u,v,f_{2}} \right)}}}} & (2)\end{matrix}$

[0048] As a result, the measured divided quantity Rexp is expressed bythe expression defined only by the electron optical state of theelectron optical system 2 without depending on characteristics ofvarious spatial frequencies of various samples 1 themselves.

[0049] Referring to FIGS. 3 through 6, the processing procedure forcarrying out the adjustment of astigmatism fa, orientation φa ofastigmatism, and the focus position (focus shifted quantity) f will bedescribed below. Herein, focusing is carried out by the focus controlpart 3, and usual astigmatism correction is carried out by the stigmater14 for correcting astigmatism. Although it does not matter whether thefocusing operation by the focus control part 3 or the astigmatismcorrecting operation by the stigmater 14 is formerly carried out, a casewhere the focusing operation is formerly carried out will be describedbelow.

[0050] First, at ST1, two STEM images I₁(x,y) 7 and I₂(x,y) 8 areacquired by shifting the focus position by a predetermined focus shiftedquantity Δf.

[0051] Then, at ST2, the Fourier transform of the acquired image iscarried out for obtaining F[I₁(x,y)] 9 and F[I₂(x,y)] 10.

[0052] Then, at ST3, division on the spatial frequency plane (u,v) iscarried out for obtaining F[I₁(x,y)]/F[I₂(x,y)] (=measured dividedquantity Rexp(u,v)).

[0053] Then, at ST4, the data processing of the measured dividedquantity Rexp(u,v) is carried out.

[0054] The step ST4 comprises a step ST4 a of carrying out thetransformation of coordinate system from (u,v) to (r, θ), a step ST4 bof averaging one-dimensional data, and a step ST4 c of carrying out asignal-noise separation.

[0055] In the data processing at ST4, the operating step of carrying outfocusing (correction of astigmatism) in the presence of astigmatism ismore complicated than the operating step of carrying out focusing in theabsence of astigmatism.

[0056] Therefore, in order to facilitate better understanding, thefocusing in the absence of astigmatism will be first described.

[0057] In the absence of astigmatism, Rexp (u,v) is transformed toRexp(r, θ) in view of the rotation symmetry of the measured dividedquantity Rexp(r, θ), and subsequently, all of radius vectordistributions Rexp(r, θ) in discrete directions θi are averaged as shownby expression ( 3 ). $\begin{matrix}{{R_{ave}(r)} = {\frac{1}{N}{\sum\limits_{i}{R_{\exp}\left( {r,\theta_{i}} \right)}}}} & (3)\end{matrix}$

[0058] As one-dimensional data, Rave(r) is obtained. Herein, N denotesthe number of discrete directions θi, and the interval between adjacentdiscrete directions θi is, e.g., 1 [degree].

[0059] Then, at the step ST4 of carrying out the signal-noiseseparation, the upper limit of the spatial frequency required to carryout the fitting of the Rave(r) to the divided quantity data 12 by thecross-correlation method is obtained as follows. First, binary images B(rj, θi) are prepared by an experimental threshold level to powerspectra. In addition, a one-dimensional radius vector counting histogramP(rj) is prepared for them (see FIG. 4 (a-2)). Using a higher relativepoint number than the threshold as a function of a spatial frequencyradius (r), this histogram is expressed as follows. $\begin{matrix}{{P\left( r_{j} \right)} = {\frac{1}{2\quad \pi \quad r_{j}}{\sum\limits_{i}{B\left( {r_{j,}\theta_{i}} \right)}}}} & (4)\end{matrix}$

[0060] From this histogram, the upper limit of the spatial frequency forcoincidence of correlation is estimated by a computer program.

[0061] Then, at ST5, the fitting of Rave(r) derived from expression ( 3) to the divided quantity data 12 is carried out by thecross-correlation method. Then, at ST6, the maximum cross-correlationcoefficient (XCCmax) is searched. Thus, the best coincident value of thefocus position f1 can be obtained (see FIGS. 5(a) and 5(b)).

[0062] Then, at ST7, the quantity of a lens current for moving the focusposition to the Scherzer focus position is calculated on the basis ofthe focus position f obtained at ST6, and this is fed back to this lenssystem. By the above described steps, the focusing in the absence ofastigmatism can be precisely carried out regardless of characteristicsof the sample 1.

[0063] The automatic focusing in the presence of astigmatism (aberrationcorrection) will be described below.

[0064] The transfer function K(u,v) has not been a circular annularpattern, and has been an elliptical annular pattern or a radial pattern.If the pattern is an elliptical ring, the difference fa in astigmatismand the focus position f can be directly obtained by measuringcharacteristic positions on major and minor axes. The f1 can be obtainedby measuring them on an intermediate axis between the major and minoraxes. The value of the focus position on the minor axis corresponds tothe maximum theoretical divided quantity, the value of the focusposition on the major axis corresponds to the minimum theoreticaldivided quantity, and an average theoretical divided quantitycorresponds to the focus position on the intermediate axis.

[0065] In the case, the data processing at ST4 is carried out asfollows.

[0066] The Rexp(u,v) is calculated, and at ST4 a, the Rexp(u,v) istransformed to the (r, θ) coordinate system to be Rexp(r, θ).Subsequently, all sets of radius vector distributions Rexp (r, θ) areaveraged in a narrow range of discrete direction θi-m<θi<θi+m, and theradius vector distribution in directions of θi is newly expressed by therespective averaged distributions as follows: $\begin{matrix}{{R_{{ave}.}\left( {r,\theta_{i}} \right)} = {\frac{1}{M}{\sum\limits_{k = {i - m}}^{i + m}\quad {E_{\exp.}\left( {r,\theta_{k}} \right)}}}} & (5)\end{matrix}$

[0067] wherein the number of additional angles from θ+m to θ−m is M. Atthis time, the additional angle |θ±m| is set to be 9 [deg].

[0068] A processing for generating discrete data every angle to separatenoise regions is carried out. Since S/N changes every angle, the noiseregions must be separated every angle. The separation of signal regionsfrom noise regions is carried out by a simple threshold processing ofintensity level of power spectra in the same manner as that in the abovedescribed expression (4). The fitting operation by correlation iscarried out in the signal region determined by the separation. FIG.4(b-1) shows a measured divided quantity Rexp in the presence ofastigmatism, and FIG. 4(b-2) shows a one-dimensional radius vectorcounting histogram P(rj) derived with respect to the discrete angularrange |θ±m| in FIG. 4 (b-1), for obtaining the upper limit of spatialfrequency, which is required to carry out the fitting of Rave(r) to thedivided quantity data by the cross-correlation method, every discreteangular range |θ±m|.

[0069] Then, the fitting operation is carried out by thecross-correlation. When focusing is carried out in the case of onlyfocus shift correction, i.e., in the absence of astigmatism, the fittingoperation of the averaged one-dimensional Rave(r, θ) in all discreteorientations to K(r;f)/K(r;f+Δf) of the theoretical model may be carriedout as shown in FIG. 3. On the other hand, in the presence ofastigmatism, Rave. (r, θi) with respect to each orientation θi is usedfor carrying out a cross-correlation operation every orientation. Thus,the focus shifted quantity having the maximum correlation coefficientevery angle θi measured by the cross-correlation is obtained. It isassumed that this is F(θi). Then, fa, φa and f are measured. In order toenhance reliability, approximation is carried out by the method of leastsquares. Since F(θi) depends on double symmetric astigmatism, it can beapproximated to the expression [f−(fa/2)cos(2θ−φa)]. Therefore,thefollowing equation can be derived. $\begin{matrix}{S = {{\sum\limits_{i}\left\lbrack {{F\left( \theta_{i} \right)} - f + {\frac{f\quad a}{2}{\cos \left( {{2\theta_{i}} - \phi_{a}} \right)}}} \right\rbrack^{2}}->\min}} & (6)\end{matrix}$

[0070] In this equation, it is not simply possible to mathematicallysolve the angle φa of astigmatism. However, it can be solved by thenumerical calculation since φa exists in the effective range of from 0to π. If φa is fixed, f and fa can be simply obtained by$\frac{\partial S}{\partial f} = {{0\quad {and}\quad \frac{\partial S}{\partial\left( {{fa}/2} \right)}} = 0}$

[0071] as follows: $\begin{matrix}{{{{{f = \frac{{DB} - {AC}}{{NB} - A^{2}}};}{{f_{a} = \frac{2\left( {{AD} - {NC}} \right)}{{NB} - A^{2}}};}{{A = {\sum\limits_{i}{\cos \left( {{2\theta_{i}} - \phi_{a}} \right)}}};}{{B = {\sum\limits_{i}{\cos^{2}\left( {{2\theta_{i}} - \phi_{a}} \right)}}};}C = {{F\left( \theta_{i} \right)}{\cos \left( {{2\theta_{i}} - \phi_{a}} \right)}}};}{{D = {\sum\limits_{i}{F\left( \theta_{i} \right)}}};}} & (7)\end{matrix}$

[0072] wherein N is the number of data of angle θi. Moreover, if θi aregiven equally at regular intervals from 0 to π (at an interval of 1[deg] at this time), A=0, and f and fa are expressed by the followingsimpler expressions.

F=D/N; fa=−2C/B  (8)

[0073] By using the above values as f and fa and comparing all of thecalculated errors S of least squares while changing φa at fine intervalsfrom 0 to π, φa is obtained. The φa having the minimum error S is theanswer. Thus, f, fa and φa are measured.

[0074] Then, the quantity of current to be adjusted with respect to eachof x and y components in the correction of astigmatism by the stigmater14 is calculated from the measured values of fa and φa to be fed back tocarry out the astigmatism correction.

[0075] If necessary, the above described process is repeated severaltimes.

[0076] Finally, the final focus correction is fed back so that thecorrected focus is the Scherzer focus.

[0077] Thus, according to this preferred embodiment, it is possible tocarry out focusing regardless of characteristics of the sample 1, sothat it is possible to obtain an image wherein astigmatism has beenprecisely corrected.

[0078] Referring to FIGS. 7 through 10, the results of experiments usinga practical apparatus will be described below.

[0079] The results obtained by repeating experiments by applying amethod for controlling the focus position of an electron microscopeaccording to the present invention are shown in FIGS. 7 through 10.

[0080]FIG. 7 shows the results of automatic focusing experiments using athin-film sample of a DRAM being a semiconductor device. First, twoHAADF-STEM images (dark-field scanning transmission electron microscopeimages by a high-angle annular-type detector) were acquired (directmagnification ×60000, 1 [pixel]=5/3 [nm]) (FIGS. 7(a) and 7(d)).Herein,after the first image (FIG. 7(a))was acquired, the focus waschanged by Δf (Δf=1.82 [Sch]) to acquire the second image (FIG. 7(b)),and the automatic adjusting method was applied thereto. FIGS. 7(b) and7(e) show power spectra obtained by the Fourier transform of the imagesof FIGS. 7(a) and 7(d). FIG. 7(c) shows the measured divided quantityRexp(u,v) obtained by division.

[0081]FIG. 8(a) shows an image after automatic focusing, and FIG. 8(b)shows power spectra obtained by the Fourier transform of the image. Evenif such a general sample was used, it was possible to confirm theoperation with high reliability.

[0082]FIG. 9 shows an experiment on automation of astigmatismcorrection. In this experiment, an Au particle deposited sample on acarbon thin film having a clear ring pattern as shown in FIGS. 2(a)through 2(h) was used in order to facilitate verification. The imageacquiring conditions are the same as those in FIG. 7. After the firstimage (FIG. 9(a) was acquired, the focus was changed by Δf to acquirethe second image (FIG. 9(b)). FIGS. 9(b) and 9(e) show power spectraobtained by the Fourier transform of the images of FIGS. 9(a) and 9(d).FIG. 9(c) shows the measured divided quantity Rexp(u,v) obtained bydivision. It is observed that crossover lines shown in FIG. 9(c) arecoincident with the major and minor axes of an ellipse very well. Afterthe results of the experiment, it was found from the results ofcalculation that the focus shifted quantity f=5.89 [Sch], astigmatismfa=2.58 [Sch] and the angle ψa=155 [deg].

[0083]FIG. 10(a) shows an image after automatic astigmatism correction,and FIG. 10(b) shows power spectra obtained by the Fourier transform ofthe image. It was found that very good astigmatism correction wascarried out.

[0084] After the results of the experiments using the practicalapparatus, it was validated that the automatic adjusting system can beoperated with high reliability in a processing time of several seconds.

[0085] From approximating calculations based on the phase contrasttransfer function (PCTF) of the transmission electron microscope image(TEM), the following expected precision (Δferror) was calculated andevaluated. It was found that the precision can approach 1 nm. TABLE 1|Δf_(error)| [Sch] Defocusf [Sch] (|Δf_(error)| [nm]) 2 −0.025(−1.4) 5 −0.11(−6.5) 15  −0.38(−22)

[0086] While the scanning transmission electron microscope (STEM) hasbeen described as an example in the above described preferredembodiment, the present invention should not be limited thereto, but theinvention maybe applied to a scanning electron microscope or atransmission electron microscope.

[0087] While the focus position has been used as an example of apredetermined physical quantity, the present invention should not belimited thereto, but the invention may be applied to another physicalquantity, e.g., an accelerating voltage of electron beams, if thephysical quantity univocally influences the focal position of anelectron microscope.

[0088] While the focusing of the electron microscope has been described,the above described technical idea should not be limited thereto, butthe idea may be applied to the control of the quantity of astigmatism.In this case, the same technique as that for detecting first and secondtwo images at two focus positions, which are realized by changing apredetermined physical quantity by a known quantity, and comparing thedetected results with theoretical data to recognize the electron opticalstate of the electron microscope to automatically adjust the focusposition may be applied for detecting first and second two images by twoastigmatism quantities, which are realized by changing a predeterminedphysical quantity by a known quantity, to compare the detected resultswith theoretical data to recognize the electron optical state of theelectron microscope to automatically adjust the quantity of astigmatism.

[0089] As described above, according to the present invention, it ispossible to carry out focusing regardless of the presence of astigmatismwithout depending on characteristics of the sample, and it is alsopossible to correct astigmatism.

1. An electron microscope comprising: an electron optical system forconducting an electron beam to a sample; a focus control part forcontrolling a focus position of said electron optical system withrespect to said sample; an image detecting part for detecting an imagecaused by said electron beam aimed at said sample; first operating meansfor spatial frequency changing each of first and second images, whichare detected by said image detecting part at two focus positions of afirst focus position and a second focus position which is a focusshifted from said first focus position and which is realized by changinga predetermined physical quantity by a known quantity, to obtain firstand second transformed images to mutually divide said first and secondtransformed images on a spatial frequency plane to derive a measureddivided quantity indicative of divided results as a function of aspatial frequency; divided quantity data previously prepared as afunction of focus positions and spatial frequencies as a set oftheoretical divided quantities, said theoretical divided quantitiesbeing obtained by deriving an image transfer function with respect tosaid electron optical system as a function of focus positions andspatial frequencies, substituting said two physical quantities, whichare shifted from each other by said known quantity, for said imagetransfer function to obtain first and second transfer function values tomutually divide said first and second transfer function values on aspatial frequency plane; and second operating means for making areference to said divided quantity data to derive said theoreticaldivided quantities, wherein functional characteristics with respect to aspatial frequency correlate to said measured divided quantity, and forderiving a focus position corresponding to the derived theoreticaldivided quantity as said first focus position, wherein the focusposition of said electron optical system is controlled by said focuscontrol part on the basis of the operated results of said secondoperating means.
 2. An electron microscope as set forth in claim 1,wherein said predetermined physical quantity is a focus position, andsaid known quantity is a focus shifted quantity between said first andsecond focus positions.
 3. An electron microscope as set forth in claim1, wherein said first operating means averages said divided results toderive said measured divided quantity as a function of a one-dimensionalspatial frequency.
 4. An electron microscope as set forth in claim 1,wherein said first operating means divides said divided results intosections of a range of values of spatial frequencies to average themevery one of said sections to derive said measured divided value as aone-dimensional spatial frequency every one of said sections, and saidsecond operating means makes a reference to said divided quantity datato derive said theoretical divided quantity, in which functionalcharacteristics with respect to a spatial frequency correlate to saidmeasured divided quantity, every one of said sections to derive anaverage theoretical divided quantity of maximum and minimum theoreticaldivided quantities of the theoretical divided quantities derived everyone of said sections, to derive a focus position corresponding to saidaverage theoretical divided quantity as said first focus position.
 5. Anelectron microscope as set forth in claim 4, which further comprises astigmater for correcting astigmatism, and wherein astigmatism iscorrected by said stigmater.
 6. An electron microscope comprising: anelectron optical system for conducting an electron beam to a sample; anastigmatism control part for controlling astigmatism of said electronoptical system with respect to said sample; an image detecting part fordetecting an image caused by said electron beam aimed at said sample;first operating means for spatial frequency changing each of first andsecond images, which are detected by said image detecting part at twoastigmatism quantity of a first astigmatism quantity and a secondastigmatism quantity which is an astigmatism quantity shifted from saidfirst astigmatism quantity and which is realized by changing apredetermined physical quantity by a known quantity, to obtain first andsecond transformed images to mutually divide said first and secondtransformed images on a spatial frequency plane to derive a measureddivided quantity indicative of divided results as a function of aspatial frequency; divided quantity data previously prepared as afunction of astigmatism quantities and spatial frequencies as a set oftheoretical divided quantities, said theoretical divided quantitiesbeing obtained by deriving an image transfer function with respect tosaid electron optical system as a function of astigmatism quantities andspatial frequencies, substituting said two physical quantities, whichare shifted from each other by said known quantity, for said imagetransfer function to obtain first and second transfer function values tomutually divide said first and second transfer function values on aspatial frequency plane; and second operating means for making areference to said divided quantity data to derive said theoreticaldivided quantities, wherein functional characteristics with respect to aspatial frequency correlate to said measured divided quantity, and forderiving an astigmatism quantity corresponding to the derivedtheoretical divided quantity as said first astigmatism quantity, whereinthe astigmatism quantity of said electron optical system is controlledby said astigmatism control part on the basis of the operated results ofsaid second operating means.
 7. A method for controlling a focusposition of an electron microscope, said method comprising: a step ofconducting an electron beam to a sample; a first operating step ofspatial frequency changing each of first and second images, which aredetected by an image detecting part at two focus positions of a firstfocus position and a second focus position, which is a focus shiftedfrom said first focus position and which is realized by changing apredetermined physical quantity by a known quantity, to obtain first andsecond transformed images to mutually divide said first and secondtransformed images on a spatial frequency plane to derive a measureddivided quantity indicative of divided results as a function of aspatial frequency, when an image caused by said electron beam aimed atsaid sample is detected by said image detecting part; a second operatingstep of deriving an image transfer function with respect to saidelectron optical system as a function of a focus position and a spatialfrequency, to substitute said two physical quantities, which are shiftedfrom each other by said known quantity, for said image transfer functionto obtain first and second transfer function values to mutually dividesaid first and second transfer function values on a spatial frequencyplane, to obtain theoretical divided quantities to make a reference todivided quantity data, which are previously prepared as a function of afocus position and a spatial frequency as a set of said theoreticaldivided quantities, to derive a focus position corresponding to thederived theoretical divided quantities as said first focus position; anda step of controlling the focus position of said electron optical systemby a focus control part, which is provided for controlling the focusposition of said electron optical system with respect to said sample, onthe basis of the results of operation at said second operating step. 8.A method for controlling a focus position of an electron microscope asset forth in claim 7, wherein said predetermined physical quantity is afocus position, and said known quantity is a focus shifted quantitybetween said first and second focus positions.
 9. A method forcontrolling a focus position of an electron microscope as set forth inclaim 7, wherein said first operating means averages said dividedresults to derive said measured divided quantity as a function of aone-dimensional spatial frequency.
 10. A method for controlling a focusposition of an electron microscope as set forth in claim 7, wherein saidfirst operating means divides said divided results into sections of arange of values of spatial frequencies to average them every one of saidsections to derive said measured divided value as a one-dimensionalspatial frequency every one of said sections, and said second operatingmeans makes a reference to said divided quantity data to derive saidtheoretical divided quantity, in which functional characteristics withrespect to a spatial frequency correlate to said measured dividedquantity, every one of said sections to derive an average theoreticaldivided quantity of maximum and minimum theoretical divided quantitiesof the theoretical divided quantities derived every one of saidsections, to derive a focus position corresponding to said averagetheoretical divided quantity as said first focus position.
 11. A methodfor controlling a focus position of an electron microscope as set forthin claim 7, wherein astigmatism is corrected by a stigmater.
 12. Amethod for controlling an astigmatism quantity of an electronmicroscope, said method comprising: a step of conducting an electronbeam to a sample; a first operating step of spatial-frequency-changingeach of first and second images, which are detected by an imagedetecting part at two astigmatism quantities of a first astigmatismquantity and a second astigmatism quantity, which is an astigmatismquantity shifted from said first astigmatism quantity and which isrealized by changing a predetermined physical quantity by a knownquantity, to obtain first and second transformed images to mutuallydivide said first and second transformed images on a spatial frequencyplane to derive a measured divided quantity indicative of dividedresults as a function of a spatial frequency, when an image caused bysaid electron beam aimed at said sample is detected by said imagedetecting part; a second operating step of deriving an image transferfunction with respect to said electron optical system as a function ofan astigmatism quantity and a spatial frequency, to substitute said twophysical quantities, which are shifted from each other by said knownquantity, for said image transfer function to obtain first and secondtransfer function values to mutually divide said first and secondtransfer function values on a spatial frequency plane, to obtaintheoretical divided quantities to make a reference to divided quantitydata, which are previously prepared as a function of an astigmatismquantity and a spatial frequency as a set of said theoretical dividedquantities, to derive an astigmatism quantity corresponding to thederived theoretical divided quantities as said first astigmatismquantity; and a step of controlling the astigmatism quantity of saidelectron optical system by a focus control part, which is provided forcontrolling the astigmatism quantity of said electron optical systemwith respect to said sample, on the basis of the results of operation atsaid second operating step.